Tools of mathematical modeling of arbitrary object packing problems

J. Bennell (), G. Scheithauer (), Y. Stoyan and T. Romanova ()

Annals of Operations Research, 2010, vol. 179, issue 1, 343-368

Abstract: The article reviews the concept of and further develops phi-functions (Φ-functions) as an efficient tool for mathematical modeling of two-dimensional geometric optimization problems, such as cutting and packing problems and covering problems. The properties of the phi-function technique and its relationship with Minkowski sums and the nofit polygon are discussed. We also describe the advantages of phi-functions over these approaches. A clear definition of the set of objects for which phi-functions may be derived is given and some exceptions are illustrated. A step by step procedure for deriving phi-functions illustrated with examples is provided including the case of continuous rotation. Copyright Springer Science+Business Media, LLC 2010

Keywords: Mathematical modeling; Cutting and packing; Phi-function; Geometry; Nofit polygon (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10479-008-0456-5

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